Uniform#
- class pylit.models.Uniform(tau, mu)#
Bases:
LinearRegressionModelThis is the linear regression model with Uniform model functions.
- kernel(omega, param)#
Evaluate the uniform kernel function for a given set of parameters.
This method overrides
kernel().- Parameters:
omega (
ndarray[float64]) – Discrete frequency axis.param (
List[float]) – Parameter tuple [k], where k indexes the interval [mu_k, mu_{k+1}] of the uniform kernel support.
- Return type:
ndarray- Returns:
Values of the uniform kernel
\[K(\omega; \mu_k, \mu_{k+1}) = \frac{\mathbf{1}_{[\mu_k, \mu_{k+1})}(\omega)}{\mu_{k+1} - \mu_k},\]
- ltransform(tau, param)#
Evaluate the Laplace-transformed uniform kernel at the discrete time axis.
This method overrides
ltransform().- Parameters:
tau (
ndarray[float64]) – Discrete time axis.param (
List[float]) – Parameter tuple [k], where k indexes the interval [mu_k, mu_{k+1}] of the uniform kernel support.
- Return type:
ndarray[float64]- Returns:
Values of the Laplace-transformed uniform kernel
\[\begin{split}\widehat{K}(\tau; \mu_k, \mu_{k+1}) = \begin{cases} 1, & \tau = 0, \\ \frac{e^{-\tau \mu_{k+1}} - e^{-\tau \mu_k}}{-\tau (\mu_{k+1}-\mu_k)}, & \tau \neq 0. \end{cases}\end{split}\]